Computational model of polarized actin cables and cytokinetic actin ring formation in budding yeast

Cooperative bundling by fascin generates actin structures with architectures that depend on filament length

The assembly of actin-based structures with precisely defined architectures supports essential cellular functions, including motility, intracellular transport, and division. The geometric arrangements of the filaments within actin structures are stabilized via the association of crosslinking proteins, which bind two filaments simultaneously. Because actin polymerization and crosslinking occur concurrently within the dynamic environment of the cell, these processes likely play interdependent roles in shaping the architectures of actin-based structures. To dissect the contribution of polymerization to the construction of higher-order actin structures, we investigated how filament elongation affects the formation of simple, polarized actin bundles by the crosslinking protein fascin. Using populations of actin filaments to represent distinct stages of elongation, we found that the rate of bundle assembly increases with filament length. Fascin assembles short filaments into discrete bundles, whereas bundles of long filaments merge with one another to form interconnected networks. Although filament elongation promotes bundle coalescence, many connections formed between elongating bundles are short-lived and are followed by filament breakage. Our data suggest that initiation of crosslinking early in elongation aligns growing filaments, creating a template for continued bundle assembly as elongation proceeds. This initial alignment promotes the assembly of bundles that are resistant to large changes in curvature that are required for coalescence into interconnected networks. As a result, bundles of short filaments remain straighter and more topologically discrete as elongation proceeds than bundles assembled from long filaments. Thus, uncoordinated filament elongation and crosslinking can alter the architecture of bundled actin networks, highlighting the importance of maintaining precise control over filament length during the assembly of specialized actin structures.

Fission Yeast Polarization: Modeling Cdc42 Oscillations, Symmetry Breaking, and Zones of Activation and Inhibition

Cells polarize for growth, motion, or mating through regulation of membrane-bound small GTPases between active GTP-bound and inactive GDP-bound forms. Activators (GEFs, GTP exchange factors) and inhibitors (GAPs, GTPase activating proteins) provide positive and negative feedbacks. We show that a reaction-diffusion model on a curved surface accounts for key features of polarization of model organism fission yeast. The model implements Cdc42 membrane diffusion using measured values for diffusion coefficients and dissociation rates and assumes a limiting GEF pool (proteins Gef1 and Scd1), as in prior models for budding yeast. The model includes two types of GAPs, one representing tip-localized GAPs, such as Rga3; and one representing side-localized GAPs, such as Rga4 and Rga6, that we assume switch between fast and slow diffusing states. After adjustment of unknown rate constants, the model reproduces active Cdc42 zones at cell tips and the pattern of GEF and GAP localization at cell tips and sides. The model reproduces observed tip-to-tip oscillations with periods of the order of several minutes, as well as asymmetric to symmetric oscillations transitions (corresponding to NETO "new end take off"), assuming the limiting GEF amount increases with cell size.

Force Production by a Bundle of Growing Actin Filaments Is Limited by Its Mechanical Properties

Bundles of actin filaments are central to a large variety of cellular structures such as filopodia, stress fibers, cytokinetic rings, and focal adhesions. The mechanical properties of these bundles are critical for proper force transmission and force bearing. Previous mathematical modeling efforts have focused on bundles' rigidity and shape. However, it remains unknown how bundle length and buckling are controlled by external physical factors. In this work, we present a biophysical model for dynamic bundles of actin filaments submitted to an external load. In combination with in vitro motility assays of beads coated with formins, our model allowed us to characterize conditions for bead movement and bundle buckling. From the deformation profiles, we determined key biophysical properties of tethered actin bundles such as their rigidity and filament density.

Organization of associating or crosslinked actin filaments in confinement

A key factor of actin cytoskeleton organization in cells is the interplay between the dynamical properties of actin filaments and cell geometry, which restricts, confines and directs their orientation. Crosslinking interactions among actin filaments, together with geometrical cues and regulatory proteins can give rise to contractile rings in dividing cells and actin rings in neurons. Motivated by recent in vitro experiments, in this work we performed computer simulations to study basic aspects of the interplay between confinement and attractive interactions between actin filaments. We used a spring-bead model and Brownian dynamics to simulate semiflexible actin filaments that polymerize in a confining sphere with a rate proportional to the monomer concentration. We model crosslinking, or attraction through the depletion interaction, implicitly as an attractive short-range potential between filament beads. In confining geometries smaller than the persistence length of actin filaments, we show rings can form by curving of filaments of length comparable to, or longer than the confinement diameter. Rings form for optimal ranges of attractive interactions that exist in between open bundles, irregular loops, aggregated, and unbundled morphologies. The probability of ring formation is promoted by attraction to the confining sphere boundary and decreases for large radii and initial monomer concentrations, in agreement with prior experimental data. The model reproduces ring formation along the flat plane of oblate ellipsoids.

Mechanical and kinetic factors drive sorting of F-actin cross-linkers on bundles

In cells, actin-binding proteins (ABPs) sort to different regions to establish F-actin networks with diverse functions, including filopodia used for cell migration and contractile rings required for cell division. Recent experimental work uncovered a competition-based mechanism that may facilitate spatial localization of ABPs: binding of a short cross-linker protein to 2 actin filaments promotes the binding of other short cross-linkers and inhibits the binding of longer cross-linkers (and vice versa). We hypothesize this sorting arises because F-actin is semiflexible and cannot bend over short distances. We develop a mathematical theory and lattice models encompassing the most important physical parameters for this process and use coarse-grained simulations with explicit cross-linkers to characterize and test our predictions. Our theory and data predict an explicit dependence of cross-linker separation on bundle polymerization rate. We perform experiments that confirm this dependence, but with an unexpected cross-over in dominance of one cross-linker at high growth rates to the other at slow growth rates, and we investigate the origin of this cross-over with further simulations. The nonequilibrium mechanism that we describe can allow cells to organize molecular material to drive biological processes, and our results can guide the choice and design of cross-linkers for engineered protein-based materials.

Multiscale model of integrin adhesion assembly

The ability of adherent cells to form adhesions is critical to numerous phases of their physiology. The assembly of adhesions is mediated by several types of integrins. These integrins differ in physical properties, including rate of diffusion on the plasma membrane, rapidity of changing conformation from bent to extended, affinity for extracellular matrix ligands, and lifetimes of their ligand-bound states. However, the way in which nanoscale physical properties of integrins ensure proper adhesion assembly remains elusive. We observe experimentally that both β-1 and β-3 integrins localize in nascent adhesions at the cell leading edge. In order to understand how different nanoscale parameters of β-1 and β-3 integrins mediate proper adhesion assembly, we therefore develop a coarse-grained computational model. Results from the model demonstrate that morphology and distribution of nascent adhesions depend on ligand binding affinity and strength of pairwise interactions. Organization of nascent adhesions depends on the relative amounts of integrins with different bond kinetics. Moreover, the model shows that the architecture of an actin filament network does not perturb the total amount of integrin clustering and ligand binding; however, only bundled actin architectures favor adhesion stability and ultimately maturation. Together, our results support the view that cells can finely tune the expression of different integrin types to determine both structural and dynamic properties of adhesions.

Mechanisms of formin-mediated actin assembly and dynamics

Cellular viability requires tight regulation of actin cytoskeletal dynamics. Distinct families of nucleation-promoting factors enable the rapid assembly of filament nuclei that elongate and are incorporated into diverse and specialized actin-based structures. In addition to promoting filament nucleation, the formin family of proteins directs the elongation of unbranched actin filaments. Processive association of formins with growing filament ends is achieved through continuous barbed end binding of the highly conserved, dimeric formin homology (FH) 2 domain. In cooperation with the FH1 domain and C-terminal tail region, FH2 dimers mediate actin subunit addition at speeds that can dramatically exceed the rate of spontaneous assembly. Here, I review recent biophysical, structural, and computational studies that have provided insight into the mechanisms of formin-mediated actin assembly and dynamics.

Structural organization and energy storage in crosslinked actin assemblies

During clathrin-mediated endocytosis in yeast cells, short actin filaments (< 200nm) and crosslinking protein fimbrin assemble to drive the internalization of the plasma membrane. However, the organization of the actin meshwork during endocytosis remains largely unknown. In addition, only a small fraction of the force necessary to elongate and pinch off vesicles can be accounted for by actin polymerization alone. In this paper, we used mathematical modeling to study the self-organization of rigid actin filaments in the presence of elastic crosslinkers in conditions relevant to endocytosis. We found that actin filaments condense into either a disordered meshwork or an ordered bundle depending on filament length and the mechanical and kinetic properties of the crosslinkers. Our simulations also demonstrated that these nanometer-scale actin structures can store a large amount of elastic energy within the crosslinkers (up to 10kBT per crosslinker). This conversion of binding energy into elastic energy is the consequence of geometric constraints created by the helical pitch of the actin filaments, which results in frustrated configurations of crosslinkers attached to filaments. We propose that this stored elastic energy can be used at a later time in the endocytic process. As a proof of principle, we presented a simple mechanism for sustained torque production by ordered detachment of crosslinkers from a pair of parallel filaments.

Computational simulation of formin-mediated actin polymerization predicts homologue-dependent mechanosensitivity

Many actin structures are nucleated and assembled by the barbed-end tracking polymerase formin family, including filopodia, focal adhesions, the cytokinetic ring and cell cortex. These structures respond to forces in distinct ways. Formins typically have profilin-actin binding sites embedded in highly flexible disordered FH1 domains, hypothesized to diffusively explore space to rapidly capture actin monomers for delivery to the barbed end. Recent experiments demonstrate that formin-mediated polymerization accelerates when under tension. The acceleration has been attributed to modifying the state of the FH2 domain of formin. Intriguingly, the same acceleration is reported when tension is applied to the FH1 domains, ostensibly pulling monomers away from the barbed end. Here we develop a mesoscale coarse-grain model of formin-mediated actin polymerization, including monomer capture and delivery by FH1, which sterically interacts with actin along its entire length. The binding of actin monomers to their specific sites on FH1 is entropically disfavored by the high disorder. We find that this penalty is attenuated when force is applied to the FH1 domain by revealing the binding site, increasing monomer capture efficiency. Overall polymerization rates can decrease or increase with increasing force, depending on the length of FH1 domain and location of binding site. Our results suggest that the widely varying FH1 lengths and binding site locations found in known formins could be used to differentially respond to force, depending on the actin structure being assembled. © 2016 Wiley Periodicals, Inc.